Problem: Simplify the following expression: $q = \dfrac{-10a + 45}{45}$ You can assume $a \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10a + 45 = - (2\cdot5 \cdot a) + (3\cdot3\cdot5)$ The denominator can be factored: $45 = (3\cdot3\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $q = \dfrac{(5)(-2a + 9)}{(5)(9)}$ Dividing both the numerator and denominator by $5$ gives: $q = \dfrac{-2a + 9}{9}$